# Thread: New question that needs help.

1. ## New question that needs help.

Here is the question im stuck on.

solve sec^2 x - (1+rt3)tan x + rt3 = 1 for the range 0< x < 4pi giving the answer in terms of pi.

Thanks

Here is the question im stuck on.

solve sec^2 x - (1+rt3)tan x + rt3 = 1 for the range 0< x < 4pi giving the answer in terms of pi.

Thanks
$\sec^2 x = \tan^2x +1$
Thus,
$\tan^2 x + 1 - (1+\sqrt{3})\tan x + \sqrt{3} = 1$
Thus,
$\tan^2 x -(1+\sqrt{3})\tan x + \sqrt{3} = 0$
Let $y=\tan x$ to get,
$y^2 - (1+\sqrt{3})y+\sqrt{y}=0$.